A block of mass m = 5.84 kg is attached to a spring with spring constant k = 1582 N/m and rests on a frictionless surface. The block is pulled, stretching the spring a distance of 0.155 m, and is held still. The block is then released and moves in simple harmonic motion about the equilibrium position. (Assume that the block is stretched in the positive direction.) (a) What is the frequency of this oscillation? _______Hz (b) Where is the block located 3.24 s after it is released? (Give the displacement from the equilibrium. Include the sign of the value in your answer.) _____m (c) What is the velocity of the mass at that time? (Indicate the direction with the sign of your answer.) ______m/s
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A block of mass m = 5.84 kg is attached to a spring with spring constant k = 1582 N/m and rests on a frictionless surface. The block is pulled, stretching the spring a distance of 0.155 m, and is held still. The block is then released and moves in simple harmonic motion about the equilibrium position. (Assume that the block is stretched in the positive direction.)
(a) What is the frequency of this oscillation? _______Hz
(b) Where is the block located 3.24 s after it is released? (Give the displacement from the equilibrium. Include the sign of the value in your answer.) _____m
(c) What is the velocity of the mass at that time? (Indicate the direction with the sign of your answer.) ______m/s
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